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faust18 [17]
2 years ago
15

What value of x makes 2x-1=-7 true?

Mathematics
1 answer:
forsale [732]2 years ago
7 0

Answer:x=-3

Step-by-step explanation:

2x-1=-7

Add 1 to each side

2x=-6

Divide each side by 2

x=-3

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Please help me with this question!
Rasek [7]

Answer:

87 packages

Step-by-step explanation:

First we need to find the volume of the cone-shaped vase.

The volume of a cone is given by:

V_cone = (1/3) * pi * radius^2 * height

With a radius of 9 cm and a height of 28 cm, we have:

V_cone = (1/3) * pi * 9^2 * 28 = 2375.044 cm3

Each package of sand is a cube with side length of 3 cm, so its volume is:

V_cube = 3^3 = 27 cm3

Now, to know how many packages the artist can use without making the vase overflow, we just need to divide the volume of the cone by the volume of the cube:

V_cone / V_cube = 2375.044 / 27 = 87.9646 packages

So we can use 87 packages (if we use 88 cubes, the vase would overflow)

5 0
3 years ago
Read 2 more answers
If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
\\\\\\
inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
\\\\\\
\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\

\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
5 0
2 years ago
If 17,000 is 47% what is 100%<br> Please explain!
Alja [10]

Answer:

36,170.21276595745 (I did this on a calculator.)

Step-by-step explanation:

17000/47 = 361.7021276595745

361.7021276595745 x 100 = 36,170.21276595745

Your total answer is 36,170.21276595745.

8 0
3 years ago
Is 3.7 an integer<br> Need help on my math homework plz help
Finger [1]
An integer is a number that is not a fraction so no 3.7 is not an integer
4 0
3 years ago
8x-2=4+5x<br><br> Solve for x
DochEvi [55]
8x-2=4+5x\ \  \ |add\ 2\ to\ both\ sides\\8x=6+5x\ \ \ \ |subtract\ 5x]\ from\ both\ sides\\3x=6\ \ \ \ |divide\ both\ sides\ by\ 3\\\boxed{x=2}
4 0
3 years ago
Read 2 more answers
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